Duca, Alessandro Joly, Romain

We consider the Schrödinger equation\begin{equation}\label{eq_abstract}i\partial_t u(t)=-\Delta u(t)~~~~~\text{ on }\Omega(t) \tag{$\ast$}\end{equation}where $\Omega(t)\subset\mathbb{R}$ is a moving domain depending on the time $t\in [0,T]$. The aim of this work is to provide a meaning to the solutions of such an equation. We use the existence of a...

guran, liliana bota, monica-felicia naseem, asim

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo / s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash / Rogers type. The second part of the paper is devoted to the study of the data depen...

boukarou, aissa guerbati, kaddour zennir, khaled alodhaibi, sultan alkhalaf, salem

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisti...

kozhanov, aleksandr i.

We study the solvability for boundary value problems to some nonlocal second-order integro&ndash / differential equations that degenerate by a selected variable. The possibility of degeneration in the equations under consideration means that the statements of the corresponding boundary value problems have to change depending on the nature of the de...

Belykh, V. N.
Published in
Computational Mathematics and Mathematical Physics

AbstractA fundamentally new—nonsaturable—method is constructed for the numerical solution of elliptic boundary value problems for the Laplace equation in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsid...

guran, liliana bota, monica-felicia naseem, asim mitrović, zoran d. de la sen, manuel radenović, stojan

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov&rsquo / s sense under a contractive condition of Hardy&ndash / Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam&ndash / Hyers stability are also studied.

Liu, Yanlin Paicu, Marius Zhang, Ping

In [15], the authors proved that as long as the one-directional derivative of the initial velocity is sufficiently small in some scaling invariant spaces, then the classical Navier-Stokes system has a global unique solution. The goal of this paper is to extend this type of result to the 3-D anisotropic Navier-Stokes system (AN S) with only horizont...

Brogliato, Bernard Tanwani, Aneel

This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations (ODEs) is coupled with a static and time-varying set-valued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems including sweeping processes, differential inclusions with maximal...

Afilal, M Guesmia, A. Soufiyane, A Zahri, M

In this paper, we consider a linear one-dimensional Bresse system consisting of three hyperbolic equations coupled in a certain manner under mixed homogeneous Dirichlet-Neumann boundary conditions. Here, we consider that only the longitudinal displacement is damped, and the vertical displacement and shear angle displacement are free. We prove the w...

Hägg, Linus

Part I. Topology optimization is the most general form of design optimization in which the optimal layout of material within a given region of space is to be determined. Filters are essential components of many successful density based topology optimization approaches. The generalized fW-mean filter framework developed in this thesis provides a uni...